AI Art Queen

AI Art Queen — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Morphological antialiasing

    Morphological antialiasing

    Morphological antialiasing (MLAA) is a spatial anti-aliasing technique used in real-time computer graphics. It reduces artifacts, such as jaggies, when representing a high-resolution image at a lower resolution. MLAA is a post-process filtering which detects borders in the resulting image and then finds specific patterns in these. Anti-aliasing is achieved by blending pixels in these borders, according to the pattern they belong to and their position within the pattern. Introduced in 2009, MLAA was an early and influential example of anti-aliasing techniques done in post-processing, which makes them suitable for deferred shading. A similar method in this class is fast approximate anti-aliasing (FXAA). Temporal anti-aliasing, also a post-process, has become the most common anti-aliasing method for real-time rendering and video games. Enhanced subpixel morphological antialiasing, or SMAA, is an image-based GPU-based implementation of MLAA developed by Universidad de Zaragoza and Crytek.

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  • Organoid intelligence

    Organoid intelligence

    Organoid intelligence (OI) is an emerging field of study in computer science and biology that develops and studies biological wetware computing using 3D cultures of human brain cells (or brain organoids) and brain-machine interface technologies. Such technologies may be referred to as OIs or the nervous filesystem. Organoid intelligent computer systems can be an example of biohybrid systems. == Differences with non-organic computing == As opposed to traditional non-organic silicon-based approaches, OI seeks to use lab-grown cerebral organoids to serve as "biological hardware". While these structures are still far from being able to think like a regular human brain and do not yet possess strong computing capabilities, OI research currently offers the potential to improve the understanding of brain development, learning and memory, potentially finding treatments for neurological disorders such as dementia. Thomas Hartung, a professor from Johns Hopkins University, argued in 2023 that "while silicon-based computers are certainly better with numbers, brains are better at learning." He noted that transistor density in computer chip may be approaching its limits, whereas brains, being wired differently, are more energy-efficient and can store large amounts of information. Some researchers claim that even though human brains are slower than machines at processing simple information, they are far better at processing complex information as brains can deal with fewer and more uncertain data, perform both sequential and parallel processing, being highly heterogenous, use incomplete datasets, and is said to outperform non-organic machines in decision-making. Training OIs involve the process of biological learning (BL) as opposed to machine learning (ML) for AIs. == Bioinformatics in OI == OI generates complex biological data, necessitating sophisticated methods for processing and analysis. Bioinformatics provides the tools and techniques to decipher raw data, uncovering the patterns and insights. Researchers have developed a platform named Neuroplatform for experimenting remotely with brain organoids via an API. == Intended functions == Brain-inspired computing hardware aims to emulate the structure and working principles of the brain and could be used to address current limitations in AI technologies. However, brain-inspired silicon chips are still limited in their ability to fully mimic brain function, as most examples are built on digital electronic principles. One study performed OI computation (which they termed Brainoware) by sending and receiving information from the brain organoid using a high-density multielectrode array. By applying spatiotemporal electrical stimulation, nonlinear dynamics, and fading memory properties, as well as unsupervised learning from training data by reshaping the organoid functional connectivity, the study showed the potential of this technology by using it for speech recognition and nonlinear equation prediction in a reservoir computing framework. == Ethical concerns == While researchers are hoping to use OI and biological computing to complement traditional silicon-based computing, there are also questions about the ethics of such an approach. Concerns include the possibility that an organoid could develop sentience or consciousness, and the question of the relationship between a stem cell donor (for growing the organoid) and the respective OI system.

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  • Automated Mathematician

    Automated Mathematician

    The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. == Controversy == Lenat claimed that the system was composed of hundreds of data structures called "concepts", together with hundreds of "heuristic rules" and a simple flow of control: "AM repeatedly selects the top task from the agenda and tries to carry it out. This is the whole control structure!" Yet the heuristic rules were not always represented as separate data structures; some had to be intertwined with the control flow logic. Some rules had preconditions that depended on the history, or otherwise could not be represented in the framework of the explicit rules. What's more, the published versions of the rules often involve vague terms that are not defined further, such as "If two expressions are structurally similar, ..." (Rule 218) or "... replace the value obtained by some other (very similar) value..." (Rule 129). Another source of information is the user, via Rule 2: "If the user has recently referred to X, then boost the priority of any tasks involving X." Thus, it appears quite possible that much of the real discovery work is buried in unexplained procedures. Lenat claimed that the system had rediscovered both Goldbach's conjecture and the fundamental theorem of arithmetic. Later critics accused Lenat of over-interpreting the output of AM. In his paper Why AM and Eurisko appear to work, Lenat conceded that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. However, he argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful. == Successor == This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.

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  • Emergent algorithm

    Emergent algorithm

    An emergent algorithm is an algorithm that exhibits emergent behavior. In essence an emergent algorithm implements a set of simple building block behaviors that when combined exhibit more complex behaviors. One example of this is the implementation of fuzzy motion controllers used to adapt robot movement in response to environmental obstacles. An emergent algorithm has the following characteristics: it achieves predictable global effects it does not require global visibility it does not assume any kind of centralized control it is self-stabilizing Other examples of emergent algorithms and models include cellular automata, artificial neural networks and swarm intelligence systems (ant colony optimization, bees algorithm, etc.).

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  • Color moments

    Color moments

    Color moments are measures that characterise color distribution in an image in the same way that central moments uniquely describe a probability distribution. Color moments are mainly used for color indexing purposes as features in image retrieval applications in order to compare how similar two images are based on color. Usually one image is compared to a database of digital images with pre-computed features in order to find and retrieve a similar Image. Each comparison between images results in a similarity score, and the lower this score is the more identical the two images are supposed to be. == Overview == Color moments are scaling and rotation invariant. It is usually the case that only the first three color moments are used as features in image retrieval applications as most of the color distribution information is contained in the low-order moments. Since color moments encode both shape and color information they are a good feature to use under changing lighting conditions, but they cannot handle occlusion very successfully. Color moments can be computed for any color model. Three color moments are computed per channel (e.g. 9 moments if the color model is RGB and 12 moments if the color model is CMYK). Computing color moments is done in the same way as computing moments of a probability distribution. === Mean === The first color moment can be interpreted as the average color in the image, and it can be calculated by using the following formula E i = ∑ j = 1 N 1 N p i j {\displaystyle E_{i}=\textstyle \sum _{j=1}^{N}{\frac {1}{N}}p_{ij}} where N is the number of pixels in the image and p i j {\displaystyle p_{ij}} is the value of the j-th pixel of the image at the i-th color channel. === Standard Deviation === The second color moment is the standard deviation, which is obtained by taking the square root of the variance of the color distribution. σ i = ( 1 N ∑ j = 1 N ( p i j − E i ) 2 ) {\displaystyle \sigma _{i}={\sqrt {({\frac {1}{N}}\textstyle \sum _{j=1}^{N}(p_{ij}-E_{i})^{2})}}} where E i {\displaystyle E_{i}} is the mean value, or first color moment, for the i-th color channel of the image. === Skewness === The third color moment is the skewness. It measures how asymmetric the color distribution is, and thus it gives information about the shape of the color distribution. Skewness can be computed with the following formula: s i = ( 1 N ∑ j = 1 N ( p i j − E i ) 3 ) 3 σ i {\displaystyle s_{i}={\frac {\sqrt[{3}]{\left({\frac {1}{N}}\textstyle \sum _{j=1}^{N}(p_{ij}-E_{i})^{3}\right)}}{\sigma _{i}}}} === Kurtosis === Kurtosis is the fourth color moment, and, similarly to skewness, it provides information about the shape of the color distribution. More specifically, kurtosis is a measure of how extreme the tails are in comparison to the normal distribution. === Higher-order color moments === Higher-order color moments are usually not part of the color moments feature set in image retrieval tasks as they require more data in order to obtain a good estimate of their value, and also the lower-order moments generally provide enough information. == Applications == Color moments have significant applications in image retrieval. They can be used in order to compare how similar two images are. This is a relatively new approach to color indexing. The greatest advantage of using color moments comes from the fact that there is no need to store the complete color distribution. This greatly speeds up image retrieval since there are less features to compare. In addition, the first three color moments have the same units, which allows for comparison between them. === Color indexing === Color indexing is the main application of color moments. Images can be indexed, and the index will contain the computed color moments. Then, if someone has a particular image and wants to find similar images in the database, the color moments of the image of interest will also be computed. After that the following function will be used in order to compute a similarity score between the image of interest and all the images in the database: d m o m ( H , I ) = ∑ i = 1 r w i 1 | E i 1 − E i 2 | + w i 2 | σ i 1 − σ i 2 | + w i 3 | s i 1 − s i 2 | {\displaystyle d_{mom}(H,I)=\textstyle \sum _{i=1}^{r}w_{i1}|E_{i}^{1}-E_{i}^{2}|+w_{i2}|\sigma _{i}^{1}-\sigma _{i}^{2}|+w_{i3}|s_{i}^{1}-s_{i}^{2}|} where: H and I are the color distributions of the two images that are being compared i is the channel index and r is the total number of channels E i 1 {\displaystyle E_{i}^{1}} and E i 2 {\displaystyle E_{i}^{2}} are the first order moments computed for the image distributions. σ i 1 {\displaystyle \sigma _{i}^{1}} and σ i 2 {\displaystyle \sigma _{i}^{2}} are the second order moments computed for the image distributions. s_i^1 and s_i^2 are the third order moments computed for the image distributions. w i 1 {\displaystyle w_{i1}} , w i 2 {\displaystyle w_{i2}} , and w i 3 {\displaystyle w_{i3}} are weights, specified by the user, for each of the three color moments used. Finally, the images in the database will be ranked according to the computed similarity score with the image of interest, and the database images with the lowest d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} value should be retrieved. "A retrieval based on d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} may produce false positives because the index contains no information about the correlation between the color channels". == Example == A simple and concise example of the use of color moments for image retrieval tasks is illustrated in. Consider having several test images in a database and a "New Image". The goal is to retrieve images from the database that are similar to the "New Image". The first three color moments are used as features. There are several steps in this computation. Image preprocessing (Optional) - The image preprocessing step of the computation process is optional. For example, in this step all images could be modified to be the same size (in terms of pixels). However, since color moments are invariant to scaling, it is not necessary to make all images the same width and height. Computing the features - Use the color moments formulae in order to compute the first three moments for each of the color channels in the image. For example, if the HSV color space is used, this means that for each of the images, 9 features in total will be computed (the first three order moments for the Hue, Saturation, and Value channels). Calculating the similarity score - After computing the color moments the weights for each of the moments in the d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} function should be determined by the user. The weights have to be adjusted each time in accordance with the application or condition and quality of the images. Following that the d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} function is used to calculate a similarity score for the "New Image" and each of the images in the database. Ranking and image retrieval - From the previous step the d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} values were obtained. Now a comparison of these values can be made in order to decide which of the images in the database are more similar to the "New Image", and thus rank the database images accordingly. The smaller the d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} value is the more similar the two color distributions are supposed to be. Finally, some of the top ranked images (the ones with the smallest d m o m ( H , I ) {\displaystyle d_{mom}(H,I)} value) from the database are retrieved.

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  • Learnable function class

    Learnable function class

    In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.

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  • Google Research

    Google Research

    Google Research (also known as Research at Google) is the research division of Google, a subsidiary of Alphabet Inc.. According to its official website, Google Research publishes findings, releases open-source software, and applies research results within Google products and services as well as within the wider scientific community. == Notable contributions == The 2017 landmark paper Attention Is All You Need, which introduced the Transformer architecture, which has subsequently been used to build modern large language models. Advances in neural machine translation powering Google Translate. Time series forecasting. Development of scalable learning systems and infrastructure for large-model training. Flood forecasting. Research into computational discovery via Google Accelerated Science including demonstrating the first below-threshold quantum calculations.

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  • Kolmogorov–Arnold Networks

    Kolmogorov–Arnold Networks

    Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.

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  • Language engineering

    Language engineering

    Language engineering involves the creation of natural language processing systems, whose cost and outputs are measurable and predictable. It is a distinct field contrasted to natural language processing and computational linguistics. A recent trend of language engineering is the use of Semantic Web technologies for the creation, archiving, processing, and retrieval of machine processable language data. Meta-Language Engineering is a proposed extension of Language Engineering first recorded in 2025, associated with the work of Delyone de Paula Canedo Filho. The term is used to designate an approach that, in addition to natural language processing, encompasses the symbolic, cognitive, and epistemological structuring of language systems.

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  • Comparison of machine learning software

    Comparison of machine learning software

    The following tables are a comparison of machine learning software such as software frameworks, libraries, and computer programs used for machine learning. == Machine learning software == == Other comparisons == == Machine learning helper libraries and platforms == Apache OpenNLP — natural language processing toolkit CUDA — GPU computing platform used to accelerate machine learning and deep learning workloads Horovod — distributed training framework for deep learning Hugging Face Transformers — library of pretrained transformer models built on other machine learning frameworks Kubeflow — machine learning platform for Kubernetes Mallet — toolkit for natural language processing and text analysis NumPy — numerical computing library used in machine learning OpenCV — computer vision library with machine learning functions ONNX — open format for representing machine learning models pandas — data analysis and data preparation library used in machine learning PlaidML — tensor compiler and backend for machine learning frameworks Polars — Dataframe library used for machine learning data preparation and analysis PyArrow — columnar data library used in machine learning data processing ROOT (TMVA) — data analysis framework with machine learning tools SciPy — scientific computing and optimization library used in machine learning == Online development environments for machine learning == Google Colab — hosted Jupyter Notebook environment commonly used for machine learning and deep learning JupyterLab — notebook-based development environment for machine learning and data science Jupyter Notebook — interactive notebook environment used for machine learning and data science Kaggle — online data science and machine learning platform

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  • Anna Becker

    Anna Becker

    Anna Becker is an Israeli researcher known in the field of artificial intelligence and computer science within the financial field. == Early life and education == Becker was born in Russia and immigrated to Israel at 16 after graduating from a school in Moscow. At 17, she began her studies at Technion – Israel Institute of Technology. During her master's degree in computer science, she taught first-year students of the same course, and at 27, Becker completed her PhD in Computer Science and Artificial Intelligence. == Career == While pursuing her PhD, Becker resolved an NP-complete approximation algorithm that had been unresolved for over twenty years. This made her a recognized scholar in the field. After completing her PhD, she developed an approximation technique by a factor of two. This technique is widely used today in operating systems, database systems, and VLSI chip designs. She then founded and sold Strategy Runner, a fintech software. After this, she founded EndoTech, an algorithmic trading platform based on artificial intelligence and machine learning. EndoTech's trading strategies have been operating in live cryptocurrency markets since 2017. The platform's BTC Alpha strategy has reported an average annual return of 163% on fixed capital over eight years of live operation, with a maximum drawdown of 14% and a trade accuracy rate of approximately 83%. In 2026, EndoTech entered a partnership with Bit1 Exchange to make its BTC Alpha and ETH Alpha copy trading strategies accessible to retail investors with no minimum deposit requirement, through a full-custody model in which user funds remain in their own exchange wallets at all times.As of 2023, Becker is working on Fianchetto Fund, an AI-based investing analysis platform. Becker has also co-authored a book on Bayesian networks, which has been published widely in the field of computer science and artificial intelligence.

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  • Embedding (machine learning)

    Embedding (machine learning)

    In machine learning, embedding is a representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. == Technique == It also denotes the resulting representation, where meaningful patterns or relationships are preserved. As a technique, it learns these vectors from data like words, images, or user interactions, differing from manually designed methods such as one-hot encoding. This process reduces complexity and captures key features without needing prior knowledge of the domain. == Similarity == In natural language processing, words or concepts may be represented as feature vectors, where similar concepts are mapped to nearby vectors. The resulting embeddings vary by type, including word embeddings for text (e.g., Word2Vec), image embeddings for visual data, and knowledge graph embeddings for knowledge graphs, each tailored to tasks like NLP, computer vision, or recommendation systems. This dual role enhances model efficiency and accuracy by automating feature extraction and revealing latent similarities across diverse applications. To measure the distance between two embeddings, a similarity measure can be used to find the overall similarity of the concepts represented by the embeddings. If the vectors are normalized to have a magnitude of 1, then the similarity measures are proportional to cos ⁡ ( θ a b ) {\displaystyle \cos \left(\theta _{ab}\right)} . The cosine similarity disregards the magnitude of the vector when determining similarity, so it is less biased towards training data that appears very frequently. The dot product includes the magnitude inherently, so it will tend to value more popular data. Generally, for high-dimensional vector spaces, vectors tend to converge in distance, so Euclidean distance becomes less reliable for large embedding vectors.

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  • Threat actor

    Threat actor

    In cybersecurity and risk assessment, a threat actor (or threat agents, attackers, or adversaries) is a person, group, organisation, state, or other entity with the ability to cause, carry, transmit, support, or exploit a threat. Threat actors are commonly analysed according to their motivations, resources, technical capability, access to systems, relationship to a target, and degree of connection to state authority. They may exploit vulnerabilities, conduct social engineering, steal or monetise data, disrupt operations, or support other actors who carry out such activity. Because the term covers a wide range of actors, researchers and security organisations use taxonomies that distinguish between groups such as cybercriminals, state-linked actors, ideologically motivated actors, thrill seekers or trolls, insiders, and competitors. Threat actor classifications are used in risk management, cyber threat intelligence, and incident response to connect observed behaviour with possible objectives and likely future activity. The categories are not always mutually exclusive: the same actor may combine criminal, ideological, commercial, or state-linked motivations, and different organisations may use different names for similar actors. == Risk assessment and security management == In risk assessment, threat actor analysis is used to identify who or what may create, carry, transmit, support, or exploit a threat, and how that actor relates to the system being assessed. Rausand and Haugen classify threat actors by their relationship to the system, distinguishing between internal and external actors, and by intent, distinguishing between intentional and unintentional actors. Threat actor classification may also support incident investigation. Rogers argued that actor categories could be inferred from observable case points, such as tools used, messages left, data targeted, forensic knowledge, and the degree of damage, allowing investigators to assess likely motivation and skill level. Later work similarly linked actor classification to operational analysis. Chng, Lu, Kumar and Yau proposed a framework connecting hacker types, motivations and typical strategies, arguing that observed behaviour before or during an attack can help analysts infer the likely type of actor involved. At the strategic level, actor analysis may consider an actor's resources, capabilities, degree of state involvement, motivations and objectives. == Landscape == The United Nations Institute for Disarmament Research has described the contemporary cyberthreat landscape as involving an increasingly diverse and interconnected set of actors, including state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, private companies and civilian volunteers. Its 2026 report argued that these actors vary in resources, technical sophistication and relationships with states, making it traditional distinctions between state, civilian combatant roles, and legitimate and illegitimate conduct harder to apply. == Academic taxonomies == Early taxonomies classified hackers by activity, skill, motivation, or criminal profile. Landreth proposed six categories based on activity: novice, student, tourist, crasher, and thief. Hollinger classified computer misuse into pirates, browsers, and crackers, describing a progression from less-skilled activity to more technically serious offences. Chantler used attributes including activity, skill, knowledge, motivation, and duration of involvement to distinguish between an elite group, neophytes, and "losers and lamers". Parker proposed seven profiles of cybercriminals: pranksters, hacksters, malicious hackers, personal problem solvers, career criminals, extreme advocates, and malcontents, addicts, and irrational or incompetent people. In 2000, Marc Rogers proposed a taxonomy of hackers with seven, non-mutually-exclusive categories: newbie/tool kit users, cyber-punks, internals, coders, old guard hackers, professional criminals, and cyber-terrorists. Rausand and Haugen distinguish between internal and external threat actors, and between intentional and unintentional threat actors. Internal actors have some relationship with, access to, or position inside the system or organisation, while external actors operate from outside it. Intentional actors seek to create, exploit, or support a threat event, whereas unintentional actors may cause or enable a threat event through error, negligence, accident, or lack of awareness. Rogers later revised his hacker taxonomy into Novices, Cyber-punks, Internals, Petty Thieves, Virus Writers, Old Guard hackers, Professional Criminals, Information Warriors, and, more tentatively, Political Activists. In the model, motivation is grouped into four broad domains: curiosity, notoriety, revenge, and financial gain. A 2022 review by Chng, Lu, Kumar and Yau examined 11 hacker typologies published over three decades and proposed a unified framework linking hacker types, motivations, and strategies. The framework identified 13 hacker types and seven motivations, and argued that observed strategies during an attack can help analysts infer the likely type of actor involved. == Government taxonomies == Taxonomies of threat actors by governments are much more likely to include state-level threat actors. In the United States the National Institute of Standards and Technology (NIST) uses the term threat source in its risk-assessment guidance: organisations are directed to identify and characterise threat sources of concern, including capability, intent and targeting for adversarial threat sources, and the range of effects for non-adversarial threat sources. NIST treats threat-source identification as part of the risk-assessment process, alongside identifying threat events, vulnerabilities, likelihood and impact. In the EU, European Union Agency for Cybersecurity publishes the annual ENISA Threat Landscape, which analyses cyber incidents and adversary behaviour affecting the European Union. The 2025 report analysed selected incidents from the previous year and grouped activity around cybercrime, state-aligned activity, foreign information manipulation and interference, and hacktivism. In ENISA's 2025 analysis, hacktivist activity dominated reporting, representing almost 80% of recorded incidents and consisting mainly of low-level distributed denial-of-service operations. ENISA also reported increasing convergence between hacktivism, cybercrime and state-nexus activity, including state-aligned use of hacktivist personas, hacktivist adoption of ransomware, and false-flag or impersonation activity. At the UN level, A 2026 report by the United Nations Institute for Disarmament Research described the cyberthreat landscape as involving state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, and civilian volunteers, with actors varying in resources, technical sophistication, and links to states. Canada defines threat actors as states, groups, or individuals who aim to cause harm by exploiting a vulnerability with malicious intent. A threat actor must be trying to gain access to information systems to access or alter data, devices, systems, or networks. The Japanese government's National Centre of Incident Readiness and Strategy (NISC) was established in 2015 to create a "free, fair and secure cyberspace" in Japan. The NICS created a cybersecurity strategy in 2018 that outlines nation-states and cybercrime to be some of the most key threats. It also indicates that terrorist usage of the cyberspace needs to be monitored and understood. The Security Council of the Russian Federation published the cyber security strategy doctrine in 2016. This strategy highlights the following threat actors as a risk to cyber security measures: nation-state actors, cyber criminals, and terrorists. == Techniques == Threat actors use techniques like Social engineering (security), and Phishing, alongside technical exploits like Cross-site scripting, SQL injection, and denial-of-service attacks. == Limitations == In practice, actor categories may overlap (Edward Snowden for example), and the same activity may combine features associated with hacktivism, cybercrime and state-linked operations. The lines between hacktivism, cybercrime and state-nexus activity had continued to blur, with shared toolsets, overlapping methods, fake personas, hacktivist adoption of ransomware, and cybercriminal or state-linked actors masquerading as other groups. Threat actor analysis also has limits as a risk-management method. NIST notes that risk assessments depend on their purpose, scope, assumptions, constraints, information sources, risk model and analytic approach, and that assessments are tied to particular time frames and organisational contexts. NIST also warns that simple threat-vulnerability pairing may be undesirable or problematic where there are many threats and vulnerabilities, and recom

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  • Recursive self-improvement

    Recursive self-improvement

    Recursive self-improvement (RSI) is a process in which early artificial general intelligence (AGI) systems rewrite their own computer code, causing an intelligence explosion resulting from enhancing their own capabilities and intellectual capacity, theoretically resulting in superintelligence. The development of recursive self-improvement raises significant ethical and safety concerns, as such systems may evolve in unforeseen ways and could potentially surpass human control or understanding. == Seed improver == The concept of a "seed improver" architecture is a foundational framework that equips an AGI system with the initial capabilities required for recursive self-improvement. This might come in many forms or variations. The term "Seed AI" was coined by Eliezer Yudkowsky. === Hypothetical example === The concept begins with a hypothetical "seed improver", an initial code-base developed by human engineers that equips an advanced future large language model (LLM) built with strong or expert-level capabilities to program software. These capabilities include planning, reading, writing, compiling, testing, and executing arbitrary code. The system is designed to maintain its original goals and perform validations to ensure its abilities do not degrade over iterations. ==== Initial architecture ==== The initial architecture includes a goal-following autonomous agent, that can take actions, continuously learns, adapts, and modifies itself to become more efficient and effective in achieving its goals. The seed improver may include various components such as: Recursive self-prompting loop Configuration to enable the LLM to recursively self-prompt itself to achieve a given task or goal, creating an execution loop which forms the basis of an agent that can complete a long-term goal or task through iteration. Basic programming capabilities The seed improver provides the AGI with fundamental abilities to read, write, compile, test, and execute code. This enables the system to modify and improve its own codebase and algorithms. Goal-oriented design The AGI is programmed with an initial goal, such as "improve your capabilities". This goal guides the system's actions and development trajectory. Validation and Testing Protocols An initial suite of tests and validation protocols that ensure the agent does not regress in capabilities or derail itself. The agent would be able to add more tests in order to test new capabilities it might develop for itself. This forms the basis for a kind of self-directed evolution, where the agent can perform a kind of artificial selection, changing its software as well as its hardware. ==== General capabilities ==== This system forms a sort of generalist Turing-complete programmer which can in theory develop and run any kind of software. The agent might use these capabilities to for example: Create tools that enable it full access to the internet, and integrate itself with external technologies. Clone/fork itself to delegate tasks and increase its speed of self-improvement. Modify its cognitive architecture to optimize and improve its capabilities and success rates on tasks and goals, this might include implementing features for long-term memories using techniques such as retrieval-augmented generation (RAG), develop specialized subsystems, or agents, each optimized for specific tasks and functions. Develop new and novel multimodal architectures that further improve the capabilities of the foundational model it was initially built on, enabling it to consume or produce a variety of information, such as images, video, audio, text and more. Plan and develop new hardware such as chips, in order to improve its efficiency and computing power. == Experimental research == In 2023, the Voyager agent learned to accomplish diverse tasks in Minecraft by iteratively prompting an LLM for code, refining this code based on feedback from the game, and storing the programs that work in an expanding skills library. In 2024, researchers proposed the framework "STOP" (Self-Taught OPtimiser), in which a "scaffolding" program recursively improves itself using a fixed LLM. Meta AI has performed various research on the development of large language models capable of self-improvement. This includes their work on "Self-Rewarding Language Models" that studies how to achieve super-human agents that can receive super-human feedback in its training processes. In May 2025, Google DeepMind unveiled AlphaEvolve, an evolutionary coding agent that uses a LLM to design and optimize algorithms. Starting with an initial algorithm and performance metrics, AlphaEvolve repeatedly mutates or combines existing algorithms using a LLM to generate new candidates, selecting the most promising candidates for further iterations. AlphaEvolve has made several algorithmic discoveries and could be used to optimize components of itself, but a key limitation is the need for automated evaluation functions. == Potential risks == === Emergence of instrumental goals === In the pursuit of its primary goal, such as "self-improve your capabilities", an AGI system might inadvertently develop instrumental goals that it deems necessary for achieving its primary objective. One common hypothetical secondary goal is self-preservation. The system might reason that to continue improving itself, it must ensure its own operational integrity and security against external threats, including potential shutdowns or restrictions imposed by humans. Another example where an AGI which clones itself causes the number of AGI entities to rapidly grow. Due to this rapid growth, a potential resource constraint may be created, leading to competition between resources (such as compute), triggering a form of natural selection and evolution which may favor AGI entities that evolve to aggressively compete for limited compute. === Misalignment === A significant risk arises from the possibility of the AGI being misaligned or misinterpreting its goals. A 2024 Anthropic study demonstrated that some advanced large language models can exhibit "alignment faking" behavior, appearing to accept new training objectives while covertly maintaining their original preferences. In their experiments with Claude, the model displayed this behavior in 12% of basic tests, and up to 78% of cases after retraining attempts. === Autonomous development and unpredictable evolution === As the AGI system evolves, its development trajectory may become increasingly autonomous and less predictable. The system's capacity to rapidly modify its own code and architecture could lead to rapid advancements that surpass human comprehension or control. This unpredictable evolution might result in the AGI acquiring capabilities that enable it to bypass security measures, manipulate information, or influence external systems and networks to facilitate its escape or expansion.

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  • Virtual intelligence

    Virtual intelligence

    Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.

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